Related papers: A note on bi-linear multipliers

Multipliers are operators that combine (frame-like) analysis, a multiplication with a fixed sequence, called the symbol, and synthesis. They are very interesting mathematical objects that also have a lot of applications for example in…

We study the space of functions $\phi\colon \NN\to \CC$ such that there is a Hilbert space $H$, a power bounded operator $T$ in $B(H)$ and vectors $\xi,\eta$ in $H$ such that $$\phi(n) = < T^n\xi,\eta>.$$ This implies that the matrix…

Let $D,X \in B(H)$ be bounded operators on an infinite dimensional Hilbert space $H$. If the commutator $[D,X] = DX-XD$ lies within $\varepsilon$ in operator norm of the identity operator $1_{B(H)}$, then it was observed by Popa that one…

In this article, we provide a multilinear version of the H\"ormander multiplier theorem with a Lorentz-Sobolev space condition. The work is motivated by the recent result of the first author and Slav\'ikov\'a where an analogous version of…

Let $V:=(\mathbb{F}_q)^d$ be a $d$-dimensional vector space over the field $\mathbb{F}_q$ of order $q$. Fix positive integers $e_1,e_2$ satisfying $e_1+e_2=d$. Motivated by analysing a fundamental algorithm in computational group theory for…

Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…

We employ a variant of Wright's circle method to determine the bivariate asymptotic behaviour of Fourier coefficients for a wide class of eta-theta quotients with simple poles in $\mathbb{H}$.

Let $E$ be a Banach function space on a probability measure space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is…

Given a multiplicative function $f$, we let $S(x,f)=\sum_{n\leq x}f(n)$ be the associated partial sum. In this note, we show that lower bounds on partial sums of divisor-bounded functions result in lower bounds on the partial sums…

We prove that if the signed binomial coefficient $(-1)^i\binom{k}{i}$ viewed modulo p is a periodic function of i with period h prime to p in the range $0\le i\le k$, then k+1 is a power of p, provided h is not too large compared to k. (In…

Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…

Similar to works of G. Ellis (1998), the concept of covering pair of Lie algebras is defined. Also, we show the existence of covering pair for the pair of Lie algebras (L,N) and then show that every crossed module is a homomorphic image of…

We prove that an injective, not necessarily bounded weighted bilateral shift operator on $\ell^2(\mathbb{Z})$ is similar to a normal operator if and only if it is similar to a scalar multiple of the simple (i.e. unweighted) bilateral shift…

We show that, if a sequence of non-zero polynomials in $\mathbb{Z}[X_1,X_2]$ take small values at translates of a fixed point $(\xi,\eta)$ by multiples of a fixed rational point within the group $\mathbb{C}\times\mathbb{C}^*$, then $\xi$…

Let U^+ be the plus part of the quantized enveloping algebra of a simple Lie algebra and let B^* be the dual canonical basis of U^+. Let b,b' be in B* and suppose that one of the two elements is a q-commuting product of quantum flag minors.…

Let $w$ be any word over the alphabet $\{0,1,\ldots, q-1\}$, and denote by $h$ either a polynomial of degree $d\geq 1$ or $h: n\mapsto m^n$ for a fixed $m$. Furthermore, denote by $e_q(w;h(n))$ the number of occurrences of $w$ as a subword…

Using the theory of functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, then, it can be expanded in terms of the product of the…

Let $E(z,s)$ be the non-holomorphic Eisenstein series for the modular group $SL(2,{\mathbb Z})$. The classical Kronecker limit formula shows that the second term in the Laurent expansion at $s=1$ of $E(z,s)$ is essentially the logarithm of…

The object of this paper is to give a systematic treatment of excedance-type polynomials. We first give a sufficient condition for a sequence of polynomials to have alternatingly increasing property, and then we present a systematic study…

We provide necessary and sufficient conditions for multilinear multiplier operators with symbols in $L^r$-based product-type Sobolev spaces uniformly over all annuli to be bounded from products of Hardy spaces to a Lebesgue space. We…